In multi-switch networks, packets (e.g., blocks of data) are routed between switches over data links shared with other traffic. In each network switch, packets are queued or buffered, resulting in variable delay. Packet delays and delay variations are caused by the queuing and scheduling processes of packets through intermediate packet switches. Much of this variation is the result of sharing a switch's queues and scheduling resources by multiple traffic flows. Though this sharing provides resource efficiency (e.g., low packet delays) for the majority of the packets, it often results in significantly longer packet delays during times of high traffic bursts and/or when large packets pass through the switches.
FIG. 1 is an illustration of packet delay variation (PDV) caused by packet propagation in a packet network. As shown, there is a narrow band of low delay packets 102. This band typically has the highest occurrence of packets with the lowest delay and delay variation. Thus, packets in this low delay band are best suited for use by adaptive timing recovery algorithms. The other packets in the distribution comprise the “long-tail” 104. These packets typically have larger delays and higher delay variation. This portion of the distribution will tend to increase (e.g., in delay and delay variation) as packets experience higher levels of queuing delay. This delay may be caused by a single switch or may be the result of multiple cascaded switches. As packets in the long-tail portion 104 of the distribution increase, packets in the low-delay band 102 will decrease (e.g., as a percentage of the total population).
Though PDV is generally modeled as having a Gaussian probability density function (PDF), this modeling may be inappropriate for stress-testing adaptive timing recovery algorithms. This is due to the fact that Gaussian PDFs tend to have the majority of values within one standard deviation of the mean. Thus, few of the values (e.g., less than 5%) at the extreme of the distribution are tested over a given time interval. For stress testing, all values of the range of interest, including the extreme values, need to be tested appropriately.
FIG. 2 is an exemplary plot of packet delays over time. In this way, FIG. 2 depicts how the delays of an exemplary packet stream of interest fluctuate when traversing multiple switches with moderate background packet traffic. In this example, there are two distinct packet delay bands—a low packet-delay band 202 and a high packet-delay band 204. The low packet-delay band 202 tends to have much lower variation (e.g., PDV) than the high packet delay-band 204.
The span and offset of the high packet-delay band 204 tends to be proportional to the amount of background packet traffic. Typically the greater the background packet traffic, the larger the band. As shown, the packets in the high packet-delay band 204 tend to occur in random bursts. In some cases, the number of packets in the high packet-delay band 204 can exceed those in the low packet-delay band.
Further, the packet-to-packet delay variation in the low packet-delay band 202 is significantly smaller than that in the high packet-delay band 204. The high packet-delay packets generally are substantially instantaneous jumps from and back to the low-packet delay band 202. Therefore, the packet-to-packet delay variations in each of these delay bands should be treated differently.
Understanding the nature of PDV caused by network devices, network equipment configurations, and live operating networks is important for designing PDV cancellation algorithms. Network emulators (e.g., PDV generators, etc.) used to create PDV on an existing packet stream are typically used in a laboratory environment to simulate delays and delay variations experienced by packets in large networks. However, these network emulators simply assume that the PDV will follow Gaussian probability density function determined by a fixed mean and fixed standard deviation. However, these network emulators do not take into account how packet delays change with varying traffic load. That is, they do not address the true delay variation of packets in networks, which tends to follow a long-tailed probability density function for packet flowing over the same path.
Accordingly, a more comprehensive approach for modeling PDV in multi-switch networks is required.